Step 1: Determine the structure of \(BCl_3\).
In \(BCl_3\), boron has three valence electrons and forms three \(B-Cl\) bonds.
The central boron atom has:
\[
3 \text{ bond pairs}
\]
and
\[
0 \text{ lone pairs}
\]
According to VSEPR theory, the steric number is
\[
3
\]
Hence, boron undergoes
\[
sp^2
\]
hybridization.
Therefore, the geometry of \(BCl_3\) is
\[
\boxed{\text{Trigonal Planar}}
\]
with bond angle
\[
120^\circ
\]
Step 2: Understand the formation of \(BCl_3 \cdot NH_3\).
\(BCl_3\) is electron deficient and acts as a Lewis acid.
Ammonia (\(NH_3\)) contains a lone pair on nitrogen and acts as a Lewis base.
Nitrogen donates its lone pair to boron:
\[
BCl_3 + NH_3 \rightarrow BCl_3 \cdot NH_3
\]
forming a coordinate covalent bond.
Step 3: Determine the geometry around boron in \(BCl_3 \cdot NH_3\).
After accepting the lone pair from nitrogen, boron is surrounded by:
\[
3 \text{ B-Cl bonds}
\]
and
\[
1 \text{ coordinate bond } (B \leftarrow NH_3)
\]
Thus, boron has
\[
4 \text{ bond pairs}
\]
and no lone pair.
The hybridization changes to
\[
sp^3
\]
which gives a
\[
\boxed{\text{Tetrahedral}}
\]
geometry around boron.
Step 4: Compare with the given options.
\[
BCl_3 \rightarrow \text{Trigonal Planar}
\]
\[
BCl_3 \cdot NH_3 \rightarrow \text{Tetrahedral}
\]
Only option (1) matches these geometries.
Step 5: Final conclusion.
Hence, the structures of
\[
BCl_3
\]
and
\[
BCl_3 \cdot NH_3
\]
are respectively
\[
\boxed{\text{Planar trigonal and Tetrahedral}}
\]
Therefore, option (1) is correct.